Multiplication by Clever Form of 1

This super handy trick lets you simplify an expression without changing its value. Which is good, because fractions should not be subject to inflation.

Sample Problem

Here's a horrible fraction. A really horrible fraction. This thing is getting coal for Christmas.

If we multiply it by 1, we won't change its value. If we multiply it by anything equivalent to 1 (such as ) we also won't change its value. Since each of our two mini-fractions has a 3 in its denominator, what happens if we multiply the whole thing by ?

Our new numerator is , and our new denominator is . Now the fraction's value hasn't changed, it looks much more manageable, and it might even get an Xbox under the tree this year.